Comparison of Experimental and Computational Simulations Results of a Pulsed Plasma Accelerator IEPC-2005-008 th Presented at the 29 International Electric Propulsion Conference, Princeton University, October 31 – November 4, 2005 T. Moeller*, D. Keefer†, R. Rhodes‡, and D. Rooney§ University of Tennessee Space Institute, Tullahoma, TN, 37388, USA and ** D. Li and C. Merkle†† Purdue University, West Lafayette, IN 47907, USA High power pulsed plasma thrusters (PPT) contain regions of high density plasma in close contact with regions of vacuum that challenge accurate numerical simulations using current MHD codes. A new version of the GEMS code has been developed to provide a method to accurately calculate these regions of disparate density. The GEMS code now includes a full Maxwell equation solver capable of providing both wave and diffusion solutions, and comparisons with analytical solutions and MACH2 simulations are given to demonstrate its accuracy. In addition, numerical calculations using GEMS illustrate the importance of a solution technique that handles all regimes from ideal insulator to good conductor. A MACH2 simulation of a simple Marshall gun thruster demonstrates the need for multiple regime computations in high power pulsed plasma thrusters. A laboratory Marshall gun thruster was developed to provide an array of diagnostic measurements that can be compared with the numerical simulations. The prototype thruster has been tested and a collection of photographic images, laser interferometer data, Rogowski coil data, and B-dot probe data was acquired. These measurements will provide data to compare with MACH2 and GEMS simulations. Nomenclature r B = magnetic induction β = pseudo-time scaling coefficient c = speed of light r E = electric field v J = current density * Research Associate Professor, Mechanical Engineering, Center for Laser Applications, [email protected]. † Professor Emeritus, Engineering Science, Center for Laser Applications, [email protected]. ‡ Research Scientist, Center for Laser Applications, [email protected]. § Graduate Research Assistant, Aerospace Engineering, [email protected]. ** Research Associate Professor, Mechanical Engineering, [email protected]. †† Reilly Professor of Engineering, Aerospace Engineering, [email protected]. 1 The 29th International Electric Propulsion Conference, Princeton University, October 31 - November 4, 2005 L = characteristic length scale t = physical time 2 VNN = von Neumann number = ∆t / µ0σ∆x ε0 = electric permittivity φB = Lagrange multiplier for divergence constraint on B field φE = Lagrange multiplier for divergence constraint on E field ρE = electric charge density σ = electrical conductivity τ = pseudo time µ0 = magnetic permeability Subscripts R = reference quantity Superscript n = physical time step k = pseudo-time step * =dimensionless variable I. Introduction Envisioned interplanetary missions that involve on-board space nuclear power systems will provide unprecedented levels of electrical power for a variety of mission needs including planetary base support, surface exploration and operations, life support and communications. The availability of this high power capability, however, also represents a challenging opportunity for the development of new, high power electric propulsion systems whose high specific impulse and high thrust levels can shorten trip times and gross vehicle weight, thereby increasing the overall attractiveness of the mission. Highly developed conventional EP thrusters such as ion engines, Hall thrusters and arcjets are well suited for lower power applications but have not been scaled to the power levels anticipated with fission-based space nuclear electric power systems. These smaller thrusters utilize electrostatic and thermal processes to provide thrust from a plasma propellant. Electromagnetic acceleration of plasmas for propulsion has long been seen as a means of providing efficient high specific impulse propulsion systems, however, development of this class of accelerators has languished because they are efficient only at power levels that heretofore have been unavailable in space. Two distinct types of electromagnetic thrusters have been suggested for the high power arena: magnetoplasmadynamic (MPD) thrusters, which are steady flow devices, and Pulsed Plasma Accelerators (PPA) that are variants of the Marshall Gun. These devices operate in different magnetic interaction regimes. The MPD operates at relatively small magnetic Reynolds number (Rm) while the PPA operates at large Rm. Pulsed systems are particularly of interest because they can be operated over a wide range of available power by varying the pulse duty cycle to retain efficient high-power operation while controlling average power. In the present paper we present initial results from a companion experimental/computational effort aimed at addressing the physical behavior and performance characteristics of high power pulsed plasma thrusters for possible applications in nuclear electric propulsion systems. The experimental portion of the program utilizes a laboratory prototype PPA that is designed to provide both detailed experimental diagnostics of PPA operation and accurate diagnostic data for validation of the companion computational simulations. The computational effort involves detailed simulations with two codes: the widely accepted MACH2 plasma dynamics code which is based on the MHD approximation and a somewhat simplified fluid dynamics capability, and a new in-house Maxwell solver known as GEMS that incorporates complete fluid dynamics capabilities and allows either MHD or full Maxwell solutions. One important role of the MACH2 code is to serve as a standard against which simulations from the newer GEMS code can be verified and to provide a historical link to the wide array of MACH2 calculations which have previously been done in our laboratory and elsewhere. Both MACH2 and GEMS are used for data interpretation and guidance to the experiments with the intention being to transfer more and more of this role to GEMS as its capabilities and consistency with MACH2 are verified. In addition, GEMS is being used to understand physics issues in areas where the MHD approximation is invalid and MACH2 cannot be used directly. The organization of the paper is a follows. Section II discusses the PPA configuration of interest and presents the details of the experimental laboratory prototype and some initial representative experimental data. Preliminary simulations of PPA operation from the MACH2 code are also presented in this section. In section III we present the electromagnetic implementation that is being used in GEMS with emphasis on a hyperbolic solution technique that is applicable to either the MHD equations of the complete Maxwell set. Section IV then presents the results of some 2 The 29th International Electric Propulsion Conference, Princeton University, October 31 - November 4, 2005 simple representative test problems that have been obtained from GEMS along with validation against closed form analytical solutions and companion MACH2 calculations. Section V summarizes our findings. II. Experiment To provide validation data for computer simulations, we are developing a laboratory prototype pulsed plasma accelerator with an emphasis on providing accurate diagnostics as opposed to optimized thruster performance. MACH2 simulations were utilized to guide the design of this prototype. This thruster has been successfully fired, and ongoing testing is providing data with which planned simulations can be compared. The experimental setup and representative data from early testing are presented in this section. A. Experimental Setup The thruster consists of a cylindrical center body 2-inches in diameter inside of a coaxial 4-inch diameter tube (Fig. 1). This outer tube is divided into a 2-inch upstream section and a 5-inch downstream section by a quartz insulating ring. The ring has sputtered metal strips connecting the two sections of the tube which, when vaporized by an ignition power supply, provides the plasma propellant that triggers and then is driven by the main power supply. The Quartz ring 17.5 µF 40 kV capacitor main power source, a 17.5 µF 40 kV capacitor charged with a 30 kV power supply, provides a maximum energy storage of almost 8 kJ with a calculated discharge time of 10 µs and an average power of nearly 800 megawatts1. Early system firing resulted in a fuse plasma that was not azimuthally uniform. To promote azimuthal symmetry, we placed axial slots in the outer electrode between the quartz fuse ring and the downstream trigger capacitor connection (Fig. 2). These slots create an array of parallel inductances between the fuse and the trigger power supply that act as an inductive divider to drive the current flowing through the electrode towards uniformity. To further promote the Thruster electrodes generation of a uniform discharge, the inner electrode was modified to include 1/8” wide slots that run almost the entire Figure 1. Photograph of prototype pulsed length of the electrode. This plasma accelerator (before adding axial slots). creates an inductive divider through which the main capacitor current must pass immediately following current initiation, rather than being delayed until the current sheet reaches the slotted section of the outer electrode downstream of the quartz fuse ring. The thruster is installed in a vacuum chamber fabricated from stainless steel tubing and plate (Fig. 3). The plasma discharges through a section Figure 2. Photograph